Without knowing whether you like to tickle the armpit or shatter shoulders, I'd start with gold dots and accubonds.Just placed an order for a 6.8SPC for my AR-5. 18" barrel 1:10 twist and I want to use it for deer in northern Michigan. Went with the 6.8 because terrain will limit shots to 200 yards.
So what's my best choice of bullets for this purpose?
I would have had interest in that cartridge had the bullet diameter been 6.5 mm, for that I would use a 129gr Nosler ABLR.
Most .277 game bullets are designed for higher velocities.
My initial research on this cartridge gave me the impression that it was designed to be a intermediate military cartridge that would out perform the 7.62x39. During it's development the 6.5mm bullet was tried while more accurate than the 6.8mm the 6.8mm was more effective with military FMJ projectiles. I have not kept up with advances in bullet tech for the 6.8 SPC but I would guess they are similar to improvements for 7.62x39 projectiles for hunting.This isn’t 2005, there are plenty of excellent hunting bullets of varying weights for 6.8 velocities now.
With this in mind, I'd recommend all of the above mentioned with the exception of the monolithic bullets, if you were wrecking bones they'd be more to the top of the list, but they're not needed, and they won't detonate the vitals as well as the others listed, at my .243 velocities, I find them acceptable but "hard" for deer, the 6.8 will do just fine with the others mentioned and I'd trust all but the sst to make 2 holes, the sst MIGHT but so far, at close range, mine just grenade a few inches after impact. I'd still put the gold dots first then accubonds, then sst, then Barnes (but push em fast!).I will be hunting from a blind, always go for the heart/lung shot behind the front shoulder, if possible, not a trophy hunter more of a grocery shopper . Need to cut joneb some slack, until I bought this AR all my hunting has been done with a 30/06 or 30/30 or a 45/70 and my assault rifle is a .44 mag Marlin lever gun.
Big believer in bigger bullets are better so 6.5 or 6.8 seem a bit puny to me but I'm willing to learn onacconda in my old age they don't punch my shoulder so much.